Open Access

ARTICLE

On Factorization of N-Qubit Pure States and Complete Entanglement Analysis of 3-Qubit Pure States Containing Exactly Two Terms and Three Terms

by Dhananjay P. Mehendale^1,*, Madhav R. Modak²

1 Department of Physics, Sir Parashurambhau College, Pune, 411030, India
2 Department of Mathematics, Sir Parashurambhau College, Pune, 411030, India

* Corresponding Author: Dhananjay P. Mehendale. Email:

Journal of Quantum Computing 2023, 5, 15-24. https://doi.org/10.32604/jqc.2023.043370

Received 30 June 2023; Accepted 24 October 2023; Issue published 05 December 2023

Abstract

A multi-qubit pure quantum state is called separable when it can be factored as the tensor product of 1-qubit pure quantum states. Factorizing a general multi-qubit pure quantum state into the tensor product of its factors (pure states containing a smaller number of qubits) can be a challenging task, especially for highly entangled states. A new criterion based on the proportionality of the rows of certain associated matrices for the existence of certain factorization and a factorization algorithm that follows from this criterion for systematically extracting all the factors is developed in this paper. 3-qubit pure states play a crucial role in quantum computing and quantum information processing. For various applications, the well-known 3-qubit GHZ state which contains two nonzero terms, and the 3-qubit W state which contains three nonzero terms, have been studied extensively. Using the new factorization algorithm developed here we perform a complete analysis vis-à-vis entanglement of 3-qubit states that contain exactly two nonzero terms and exactly three nonzero terms.

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Keywords

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